Research On Constrained Multi-objective Optimization Problems Based On Evolutionary Algorithms

Constrained multi-objective optimization problems widely exist in the real world,and many engineering problems can eventually be modeled as a constrained multi-objective optimization problem.For example,the wing design of an aircraft requires high safety,but also requires high quality,easy maintenance,and so on.When we subdivide the objectives of safety and quality,the designer must weigh a series of objectives such as the shape of the wing,building materials,and structure.In addition to these objectives,there are a series of constraints that restrict the designer.Such as investment capital,the upper limit of quality of building materials,and so on.There are two main challenges in constrained multi-objective optimization problems.The first challenge: multi-objective optimization.Different from single-objective optimization problems,multi-objective optimization problems often face conflicts between objectives,and it is always impossible to achieve the optimum on all objectives at the same time.This requires a well-designed algorithm to obtain a set of welldistributed Pareto optimal solutions.The second challenge: constraints.When a multiobjective problem has constraints,the problem tends to become more complicated.For example,the feasible region in the target space becomes discontinuous and difficult to find,or the feasible region becomes extremely small and difficult to find.There are even many local optimal traps that make it difficult for the algorithm to converge to the true Pareto front.Because of the above two challenges,evolutionary algorithm as a heuristic algorithm has replaced traditional optimization methods and has been widely used.In this paper,combining the research status at home and abroad,two types of evolutionary algorithms are proposed to solve the constrained multi-objective optimization problems.The following is the main contributions in this paper:1.An evolutionary algorithm based on non-dominated sorting and an improved niching method is proposed.To solve the situation where too many constraints make the feasible region narrow or discrete,the information of the infeasible solutions is particularly important.This algorithm proposes a new constraint handling technique to deal with the problems that have many constraints,and this constraint handling technique is called MC-CHT.MC-CHT first sorts the constraints according to the constraint capability,and then adds them one by one during the evolution process from difficult to easy,among which the difficult to easy is to reduce meaningless searches in infeasible areas.Combining MC-CHT with econstraints can make use of more infeasible solution information in the early stage.With the increase in the number of constraints added,the population is gradually approaching towards the true Pareto front.Finally,an improved niching method is proposed in the environmental selection to increase the diversity of each generation population,and eventually obtain a set of Pareto optimal solutions with wide distribution and good convergence.We call the algorithm MC-MOEA and comparing it with the state-of-the-art algorithms,the proposed algorithm is effective.2.An evolutionary algorithm based on a collaborative framework and two-stage evolution is proposed.To deal with the problems that have local optimal traps,the algorithm uses the different tendency selection of two populations in co-evolution so that the populations can jump out of the trap and approach the real Pareto front.Specifically,during the process of evolution,one population considers constraints while the other population does not consider constraints.In this way,when the population that considers constraints converges to the local optimal trap,the individual information of the population with no constraints can help the previous population jump out of the trap and continue to evolve.Then a two-stage evolution strategy is proposed on this basis,that is,the number of offspring produced by the two populations at different stages is different.Through this strategy,the population can selectively make a broader global search in the early stage,and quickly converge to the Pareto front of the feasible region in the later stage.Finally,a niching method based on the reference vector is designed,by which the individuals who are most likely to produce offspring distributed in the sparse area can be selected,so that the population can find all feasible areas.The numerical experiment results show that the algorithm has good performance compared with the state-of-the-art algorithms.